\(\int { { {\sec }^{3}}xdx}\)=( )
A: \(\frac{1}{2}\sec x\cot x-\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\)
B: \(\frac{1}{2}\sec x\tan x+\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\)
C: \(-\frac{1}{2}\csc x\tan x+\frac{1}{2}\ln \left| \sec x-\cot x \right|+C\)
D: \(-\frac{1}{2}\sec x\tan x-\frac{1}{2}\ln \left| \csc x+\tan x \right|+C\)
A: \(\frac{1}{2}\sec x\cot x-\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\)
B: \(\frac{1}{2}\sec x\tan x+\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\)
C: \(-\frac{1}{2}\csc x\tan x+\frac{1}{2}\ln \left| \sec x-\cot x \right|+C\)
D: \(-\frac{1}{2}\sec x\tan x-\frac{1}{2}\ln \left| \csc x+\tan x \right|+C\)
举一反三
- \( \int {\sec xdx} \)=( )。 A: \( \ln \left| {\csc x + \tan x} \right| + C \) B: \( \ln \left| {\sec x + \cot x} \right| + C \) C: \( \ln \left| {\sec x + \tan x} \right| + C \) D: \( \ln \left| {\csc x + \cot x} \right| + C \)
- 不定积分$\int<br/>\tan ^{3}x \sec x\text{d}x=$( ) A: $\frac{1}{3} \sec^3 x+\sec x+C$ B: $\frac{1}{3} \sec^3 x-\sec x+C$ C: $\sec^3 x-\sec x+C$ D: $\sec^3 x+\sec x+C$
- 不定积分$\int<br/>\tan ^{2}x \sec^{2}x\text{d}x=$( ) A: $\frac{1}{3}{{\tan }^{3}}x+C$ B: $-\frac{1}{3}{{\tan }^{3}}x+C$ C: $\frac{1}{3}{{\sec }^{3}}x+C$ D: $-\frac{1}{3}{{\sec }^{3}}x+C$
- \(\int { { {\tan }^{10}}x { { \sec }^{2}}xdx}\)=( ) A: \(-\frac{1}{11} { { \tan }^{11}}x+C\) B: \(\frac{1}{11} { { \tan }^{11}}x+C\) C: \(\frac{1}{11} { { \cot }^{11}}x+C\) D: \(-\frac{1}{11} { { \cot }^{11}}x+C\)
- 3. 已知函数$y= \tan x$，则$y''(x) =$( )。 A: $ - \sec ^ 2 x \tan x$ B: $ \sec ^ 2 x \tan x$ C: $ - 2 \sec ^ 2 x \tan x$ D: $2 \sec ^2 x \tan x$